1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Density of states

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data

    We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by

    [tex]\psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L) [/tex]

    [tex]\psi(x) = \psi(x + L)[/tex]

    What is the density of states at the Fermi level for this metal?

    3. The attempt at a solution

    According to my book, the total energy of the system is

    [tex]E = \frac{\hbar^{2}\pi^{2}n^{2}}{2mL^{2}}[/tex]

    why is this?

    It's evident that k = n*2*pi because of the boundary contidions. I don't know what to do next.
    Last edited: Dec 7, 2008
  2. jcsd
  3. Dec 8, 2008 #2


    User Avatar
    Homework Helper

    That doesn't look right to me. What book is this? Isn't that the energy of a SINGLE electron in the energy mode n (not the energy of all of them together)?

    However, I think this expression will still be useful to you, because, since you are ignoring spin, then a single electron fills an energy level, so it represents dE/dN, where N is the number of electrons in the system.
    Last edited: Dec 8, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook